In this short post, we are going to solve a few problems involving Uniform Distribution. Uniform Distribution is yet another favorite of many interviewers, and nailing any problems involving Uniform Distribution really makes your candidacy stand out

*We are continuing our series on cracking Data Science interviews. So far, we have worked out a [few_](https://medium.com/swlh/linear-regression-and-maximum-likelihood-1dcb9435c71e)[_examples_](https://medium.com/swlh/maximum-likelihood-and-data-science-interviews-c31b1d5b4e4a)* on Maximum Likelihood Estimator (MLE). In this short post, we are going to solve a few problems involving Uniform Distribution. Uniform Distribution is yet another favorite of many interviewers, and nailing any problems involving Uniform _Distribution really makes your candidacy stand out đź™‚

A uniform distribution over the bounds a and b has the following probability density function:

Probability Density Function of Uniform Distribution

Here is the curve for the pdf from Wikipedia:

Recall that the**_ Cumulative Distribution Function (CDF) _**of a uniform distribution is given by

Cumulative Distribution Function of Uniform Distribution

We are going to use the CDF (instead of PDF) a lot in this post! Make sure you understand the formula above.

Finally, we are mainly going to deal with a Uniform Distribution over the interval [0, 1]. We are also going to ignore the range outside the interval [0, 1]. The formulae for PDF and CDF simplify to the following forms for this simple interval:

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